{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## _*VQE; using its callback to monitor optimization progress*_\n",
    "\n",
    "This notebook demonstrates using Qiskit Aqua's VQE algorithm to plot graphs of the convergence path to ground state energy with different optimizers.\n",
    "\n",
    "This notebook uses the callback capability of VQE to capture information at each objective functional evaluation where it is computing the energy using the parameterized variational form. While the params themselves are also part of the callback we are only interested in the energy value here to plot the convergence. \n",
    "\n",
    "Note: other variational algorithms such as QAOA and QSVM have similar callbacks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pylab\n",
    "\n",
    "from qiskit import BasicAer\n",
    "from qiskit.aqua.operators import WeightedPauliOperator\n",
    "from qiskit.aqua import QuantumInstance, aqua_globals\n",
    "from qiskit.aqua.algorithms import VQE, NumPyMinimumEigensolver\n",
    "from qiskit.aqua.components.initial_states import Zero\n",
    "from qiskit.aqua.components.optimizers import COBYLA, L_BFGS_B, SLSQP\n",
    "from qiskit.circuit.library import TwoLocal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we create a qubit operator for VQE. Here we have taken a set of paulis that were originally computed by qiskit-chemistry for an H2 molecule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pauli_dict = {\n",
    "    'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": -1.052373245772859}, \"label\": \"II\"},\n",
    "              {\"coeff\": {\"imag\": 0.0, \"real\": 0.39793742484318045}, \"label\": \"ZI\"},\n",
    "              {\"coeff\": {\"imag\": 0.0, \"real\": -0.39793742484318045}, \"label\": \"IZ\"},\n",
    "              {\"coeff\": {\"imag\": 0.0, \"real\": -0.01128010425623538}, \"label\": \"ZZ\"},\n",
    "              {\"coeff\": {\"imag\": 0.0, \"real\": 0.18093119978423156}, \"label\": \"XX\"}\n",
    "              ]\n",
    "}\n",
    "\n",
    "qubit_op = WeightedPauliOperator.from_dict(pauli_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we loop over the set of optimizers. The defaults for maxiters/evals for the respective optimizers is more than sufficient to converge the above H2 problem so we do not need to add any logic to set accordingly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization complete      \n"
     ]
    }
   ],
   "source": [
    "optimizers = [COBYLA, L_BFGS_B, SLSQP]\n",
    "converge_cnts = np.empty([len(optimizers)], dtype=object)\n",
    "converge_vals = np.empty([len(optimizers)], dtype=object)\n",
    "num_qubits = qubit_op.num_qubits\n",
    "\n",
    "for i in range(len(optimizers)):\n",
    "    aqua_globals.random_seed = 250\n",
    "    optimizer = optimizers[i]()\n",
    "    print('\\rOptimizer: {}        '.format(type(optimizer).__name__), end='')\n",
    "    init_state = Zero(num_qubits)\n",
    "    var_form = TwoLocal(num_qubits, 'ry', 'cz', initial_state=init_state)\n",
    "\n",
    "    counts = []\n",
    "    values = []\n",
    "    def store_intermediate_result(eval_count, parameters, mean, std):\n",
    "        counts.append(eval_count)\n",
    "        values.append(mean)\n",
    "  \n",
    "    algo = VQE(qubit_op, var_form, optimizer, callback=store_intermediate_result)\n",
    "    backend = BasicAer.get_backend('statevector_simulator')\n",
    "    quantum_instance = QuantumInstance(backend=backend)  \n",
    "    algo_result = algo.run(quantum_instance)\n",
    "    converge_cnts[i] = np.asarray(counts)\n",
    "    converge_vals[i] = np.asarray(values)\n",
    "print('\\rOptimization complete      ');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now from the callback data we stored we can plot the energy value at each objective function call each optimzer makes. An optimizer using a finite difference method for computing gradient has that characteristic step like plot where for a number of evaluations it is computing the value for close by points to establish a gradient (the close by points having very similiar values whose difference cannot be seen on the scale of the graph here)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x133d58650>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "for i in range(len(optimizers)):\n",
    "    pylab.plot(converge_cnts[i], converge_vals[i], label=optimizers[i].__name__)\n",
    "pylab.xlabel('Eval count')\n",
    "pylab.ylabel('Energy')\n",
    "pylab.title('Energy convergence for various optimizers')\n",
    "pylab.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally since the above problem is still easily tractable classically we can use NumPyMinimumEigensolver to compute a reference value for the solution. We can now plot the difference from the resultant exact solution as the energy converges with VQE towards the minimum value which should be that exact classical solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value: -1.8572750302023797\n"
     ]
    }
   ],
   "source": [
    "ee = NumPyMinimumEigensolver(qubit_op)\n",
    "result = ee.run()\n",
    "ref = result.eigenvalue.real\n",
    "print('Reference value: {}'.format(ref))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x133f35b10>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.rcParams['figure.figsize'] = (12, 8)\n",
    "for i in range(len(optimizers)):\n",
    "    pylab.plot(converge_cnts[i], abs(ref - converge_vals[i]), label=optimizers[i].__name__)\n",
    "pylab.xlabel('Eval count')\n",
    "pylab.ylabel('Energy difference from solution reference value')\n",
    "pylab.title('Energy convergence for various optimizers')\n",
    "pylab.yscale('log')\n",
    "pylab.legend(loc='upper right')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
